Slalom UK website explains all you need to know about slalom in the UK.
Typical event format is to have practice and then there are two timed runs. The best one counts. There are time penalties for hitting posts (2 seconds) or missing gates (50 seconds). The courses seem to take under 3 minutes to complete but it is a high adrenaline sprint through the gates. Performed on moving water it's great skill training for river running. The beginners events have gentle currents while the premier events have seriously violent water!
See Slalom Technique for online video coaching K1, C1 and C2. See Helen Reeves guide to slalom from the Olympics here and Campbell Walsh gives his top tips on slalom kayaking here. Also Evil in the Upstreams by the ICF is a good development series to learn from.
Cool Blue Canoes Suppliers of the excellent Galasport slalom kayaks and canoes and polo kayaks too.